Could you get your period while you're pregnant?

Yes. A flow very much like a menstrual cycle can occur during pregnancy. It is not cyclical like a menstrual flow, and is not associated with ovulation, but rather may indicate a problem with the placenta.
No. Menstruation, defined strictly, is not possible during pregnancy. On the other hand, vaginal bleeding due to other causes is common, often leading to confusion. Not all vaginal bleeding, whether pregnant or not, is a 'period.'.